A robust fixed random walk technique is developed in this paper to solve one-dimensional heat equation subject to Dirichlet boundary conditions. A convenient finite difference scheme was built to direct a random moving of particles not only parallel to the mesh axes in the solution region but also in diagonal directions to allow particles walk termination at the corner points and include them in the calculation. Results have been computed via a simple precision FORTRAN code and compared with both exact solutions and ordinary fixed random walk. A good agreement was found for various cases.